; ex_2_1

(define (make-rat3 n d)
  (let ((g ((if (< d 0) - +) (gcd n d))))
    (cons (/ n g) (/ d g))))

; 2.1.1

; operation
(define (add-rat x y)
  (make-rat (+ (* (numer x) (denom y))
               (* (numer y) (denom x)))
            (* (denom x) (denom y))))
(define (sub-rat x y)
  (make-rat (- (* (numer x) (denom y))
               (* (numer y) (denom x)))
            (* (denom x) (denom y))))
(define (mul-rat x y)
  (make-rat (* (numer x) (numer y))
            (* (denom x) (denom y))))
(define (div-rat x y)
  (make-rat (* (numer x) (denom y))
            (* (numer y) (denom x))))
(define (equal-rat? x y)
  (= (* (numer x) (denom y))
     (* (numer y) (denom x))))

; constructor, selector
(define (make-rat n d) (cons n d))
(define (numer x) (car x))
(define (denom x) (cdr x))

(define (print-rat x)
  (newline)
  (display (numer x))
  (display "/")
  (display (denom x)))

(define (make-rat2 n d)
  (let ((g (gcd n d)))
    (cons (/ n g) (/ d g))))